Singular Learning Theory uses the Local Learning Coefficient to quantify neural network loss landscape geometry, but mean-energy estimators rely on an additive loss baseline. During off-equilibrium training phases, this minimum is unknown, and substituting it with noisy mini-batch losses introduces systematic minimization bias. The authors propose the Shift-Invariant Variance Estimator (SIVE) to structurally eliminate this unknown baseline through the variance operator. By combining SIVE with a correction derived from the Law of Total Variance, the method separates geometric loss fluctuations from evaluation noise. Controlled experiments on analytically tractable toy models demonstrate that SIVE recovers expected finite-temperature geometric signals where anchored mean estimators fail. Applied to deep neural networks, SIVE serves as a robust diagnostic for tracking structural phase transitions throughout training.